Uncertainty in ellipse fitting using a flatbed scanner: development and experimental verification

In the field of dimensional metrology, the use of optical measuring machines requires the handling of a large number of measurement points, or scanning points, taken from the image of the measurand. The presence of correlation between these measurement points has a significant influence on the uncertainty of the result. The aim of this work is the development of an estimation procedure for the uncertainty of measurement in a geometrically elliptical shape, taking into account the correlation between the scanning points. These points are obtained from an image produced using a commercial flat bed scanner. The characteristic parameters of the ellipse (coordinates of the center, semi-axes and the angle of the semi-major axis with regard to the horizontal) are determined using a least squares fit and orthogonal distance regression. The uncertainty is estimated using the information from the auto-correlation function of the residuals and is propagated through the fitting algorithm according to the rules described in Evaluation of Measurement Data—Supplement 2 to the ‘Guide to the Expression of Uncertainty in Measurement’—Extension to any number of output quantities. By introducing the concept of cut-off length, it can be observed how it is possible to take into account the presence of the correlation in the estimation of uncertainty in a very simple way while avoiding underestimation.

A fitting algorithm for random modeling the PLC channel

The characteristics of the power-line communication (PLC) channel are difficult to model due to the heterogeneity of the networks and the lack of common wiring practices. To obtain the full variability of the PLC channel, random channel generators are of great importance for the design and testing of communication algorithms. In this respect, we propose a random channel generator that is based on the top-down approach. Basically, we describe the multipath propagation and the coupling effects with an analytical model. We introduce the variability into a restricted set of parameters and, finally, we fit the model to a set of measured channels. The proposed model enables a closed-form description of both the mean path-loss profile and the statistical correlation function of the channel frequency response. As an example of application, we apply the procedure to a set of in-home measured channels in the band 2-100 MHz whose statistics are available in the literature. The measured channels are divided into nine classes according to their channel capacity. We provide the parameters for the random generation of channels for all nine classes, and we show that the results are consistent with the experimental ones. Finally, we merge the classes to capture the entire heterogeneity of in-home PLC channels. In detail, we introduce the class occurrence probability, and we present a random channel generator that targets the ensemble of all nine classes. The statistics of the composite set of channels are also studied, and they are compared to the results of experimental measurement campaigns in the literature.

An application of the finite element method to curve fitting

An application of the Finite Element Method (FEM) to the solution of a geometric problem is shown. The problem is related to curve fitting i.e. pass a curve trough a set of given points even if they are irregularly spaced. Situations where cur ves with cusps can be encountered in the practice and therefore smooth interpolatting curves may be unsuitable. In this paper the possibilities of the FEM to deal with this type of problems are shown. A particular example of application to road planning is discussed. In this case the funcional to be minimized should express the unpleasent effects of the road traveller. Some comparative numerical examples are also given.

Surface fitting in geomorphology - examples for regular-shaped volcanic landforms

In nature, several types of landforms have simple shapes: as they evolve they tend to take on an ideal, simple geometric form such as a cone, an ellipsoid or a paraboloid. Volcanic landforms are possibly the best examples of this ?ideal? geometry, since they develop as regular surface features due to the point-like (circular) or fissure-like (linear) manifestation of volcanic activity. In this paper, we present a geomorphometric method of fitting the ?ideal? surface onto the real surface of regular-shaped volcanoes through a number of case studies (Mt. Mayon, Mt. Somma, Mt. Semeru, and Mt. Cameroon). Volcanoes with circular, as well as elliptical, symmetry are addressed. For the best surface fit, we use the minimization library MINUIT which is made freely available by the CERN (European Organization for Nuclear Research). This library enables us to handle all the available surface data (every point of the digital elevation model) in a one-step, half-automated way regardless of the size of the dataset, and to consider simultaneously all the relevant parameters of the selected problem, such as the position of the center of the edifice, apex height, and cone slope, thanks to the highly performing adopted procedure. Fitting the geometric surface, along with calculating the related error, demonstrates the twofold advantage of the method. Firstly, we can determine quantitatively to what extent a given volcanic landform is regular, i.e. how much it follows an expected regular shape. Deviations from the ideal shape due to degradation (e.g. sector collapse and normal erosion) can be used in erosion rate calculations. Secondly, if we have a degraded volcanic landform, whose geometry is not clear, this method of surface fitting reconstructs the original shape with the maximum precision. Obviously, in addition to volcanic landforms, this method is also capable of constraining the shapes of other regular surface features such as aeolian, glacial or periglacial landforms.

Determination of Maximum Mechanical Energy Efficiency in Energy Galloping Systems

Transverse galloping is a type of aeroelastic instability characterized by large amplitude, low frequency, normal to wind oscillations that appear in some elastic two-dimensional bluff bodies when subjected to a fluid flow, provided that the flow velocity exceeds a threshold critical value. Such an oscillatory motion is explained because of the energy transfer from the flow to the two-dimensional bluff body. The 7 amount of energy that can be extracted depends on the cross section of the galloping prism. Assuming that the Glauert-Den Hartog quasistatic criterion for galloping instability is satisfied in a first approximation, the suitability of a given cross section for energy harvesting is evaluated by analyzing the lateral aerodynamic force coefficient, fitting a function with a power series in tan a (a being the angle of attack) to 10 available experimental data. In this paper, a fairly large number of simple prisms (triangle, ellipse, biconvex, and rhombus cross sections, as well 11 as D-shaped bodies) is analyzed for suitability as energy harvesters. The influence of the fitting process in the energy harvesting efficiency evaluation is also demonstrated. The analysis shows that the more promising bodies are those with isosceles or approximate isosceles cross sections.

Assessment of diastolic chamber properties of the right ventricle by global fitting of pressure-volume data and conformational analysis of 3D + T echocardiographic sequences

Assessment of diastolic chamber properties of the right ventricle by global fitting of pressure-volume data and conformational analysis of 3D + T echocardiographic sequences

Deciduous tree reconstruction algorithm based on cylinder fitting from mobile terrestrial laser scanned point clouds

Vector reconstruction of objects from an unstructured point cloud obtained with a LiDAR-based system (light detection and ranging) is one of the most promising methods to build three dimensional models of orchards. The cylinder fitting method for woody structure reconstruction of leafless trees from point clouds obtained with a mobile terrestrial laser scanner (MTLS) has been analysed. The advantage of this method is that it performs reconstruction in a single step. The most time consuming part of the algorithm is generation of the cylinder direction, which must be recalculated at the inclusion of each point in the cylinder. The tree skeleton is obtained at the same time as the cluster of cylinders is formed. The method does not guarantee a unique convergence and the reconstruction parameter values must be carefully chosen. A balanced processing of clusters has also been defined which has proven to be very efficient in terms of processing time by following the hierarchy of branches, predecessors and successors. The algorithm was applied to simulated MTLS of virtual orchard models and to MTLS data of real orchards. The constraints applied in the method have been reviewed to ensure better convergence and simpler use of parameters. The results obtained show a correct reconstruction of the woody structure of the trees and the algorithm runs in linear logarithmic time